A modified Tolman mass-energy formula

A modified Tolman mass (energy) formula is derived for spherically symmetric, time-independent systems. In the absence of surfaces of discontinuity, the modified formula has, in contradistinction to the original formula, the following desirable properties: (i) it always gives the correct mass of the system as a whole; (ii) it always gives the correct mass of any portion of the system which is surrounded by vacuum; and (iii) it remains invariant under a rescaling of the time coordinate of the formt Ct, C=constant. In the presence of surfaces of discontinuity the Tolman mass formula is further modified by the addition of the Israel mass associated with each surface. The resulting formula also has the above three properties. A new exact solution of Einstein's equations which is well behaved everywhere and is, in a sense, a generalization of Florides' new interior Schwarzschild solution is also presented.This result explains why, takingT ₁ ¹ =[C] in Section 2, we were able to obtain a solution free of surfaces of discontinuity.     

Volume matching in Tolman models

Since the equations of general relativity are nonlinear, it is not strictly correct to obtain average values by integrating over spatial volumes. Yet this is really what is done in the attempt to fit our rather lumpy universe to a standard cosmological model of uniform density. Consequently, the fitting problem, raised last year by Ellis and Stoeger [1], asks how accurate the average values derived from observational cosmology can be, even without measurement uncertainties. Do they really describe the best-fit Robertson-Walker model to our universe? One of the alternatives to averaging they suggested was that of volume matching. We try to provide a first estimate of the error due to averaging by fitting a Robertson-Walker model to an inhomogeneous Tolman model using realistic density profiles. Comparing the results from volume matching and from averaging, we find that errors are of the order of 10% or more.     

A quantal toy model for heavy-ion collisions

A one-dimensional toy model of two moving finite boxes is analysed with respect to quantal phenomena associated with heavy-ion dynamics at low and intermediate energies. Special attention is payed to the relation between energy and momentum of the nucleons inside and outside the time-dependent mean field. A Wigner transformation of the one-body density matrix in space and time allows for a unique comparison with classical phase-space dynamics. It is found that high momentum components of the nuclear groundstate wave function approximately become on-shell during the heavy-ion reaction. This leads to the emission of energetic nucleons which do not appear classically. It is furthermore shown, that the low lying eigenstates of the dinuclear system for fixed time are only partly occupied throughout the reaction at intermediate energies. This opens up final phase space for nucleons after producing e.g. a pion or energetic photon. Though the present model does not allow for a reliable calculation of double differential nucleon spectra, pion or photon cross sections, it transparently shows the peculiar features of quantum dynamics in heavy-ion collisions.     

A quantal treatment of octupole Coulomb-nuclear interference

A quantal DWBA calculation of Coulomb-nuclear interference, for excitations of arbitrary multipolarity, has been developed. Data for ²⁰⁸Pb(α, ′α)²⁰⁸Pb (3^?) at 21 and 22 MeV are presented and analyzed. The theory fits these and other data well.     

Strange quark star with Tolman IV background

In this paper, using the optical emission spectroscopy (OES) technique, the optical characteristics of a radiofrequency (RF) plasma jet are examined. The \(\hbox {Ar}/\hbox {O}_{2}\) mixture is taken as the operational gas and, the Ar percentage in the \(\hbox {Ar}/\hbox {O}_{2}\) mixture is varied from 70% to 95%. Using the optical emission spectrum analysis of the RF plasma jet, the excitation temperature is determined based on the Boltzmann plot method. The electron density in the plasma medium of the RF plasma jet is obtained by the Stark broadening of the hydrogen Balmer \(H_{\beta }\). It is mostly seen that, the radiation intensity of Ar 4p\(\rightarrow \)4s transitions at higher argon contributions in \(\hbox {Ar}/\hbox {O}_{2}\) mixture is higher. It is found that, at higher Ar percentages, the emission intensities from atomic oxygen (O) are higher and, the line intensities from the argon atoms and ions including O atoms linearly increase. It is observed that the quenching of \(\hbox {Ar}^{*}\) with \(\hbox {O}_{2}\) results in higher O species with respect to \(\hbox {O}_{2}\) molecules. In addition, at higher percentages of Ar in the \(\hbox {Ar}/\hbox {O}_{2}\) mixture, while the excitation temperature is decreased, the electron density is increased.     

A problem of information gain by quantal measurements

For the average information gain by a quantal measurement of the first kind, an expression is suggested for a lower bound, which turns out to be non-negative.     

A new Tolman test of a cosmic distance duality relation at 21 cm

Under certain general conditions in an expanding universe, the luminosity distance (d(L)) and angular diameter distance (d(A)) are connected by the Etherington relation as d(L)=d(A)(1+z)2. The Tolman test suggests the use of objects of known surface brightness, to test this relation. In this Letter, we propose the use of a redshifted 21 cm signal from disk galaxies, where neutral hydrogen (HI) masses are seen to be almost linearly correlated with surface area, to conduct a new Tolman test. We construct simulated catalogs of galaxies, with the observed size-luminosity relation and realistic redshift evolution of HI mass functions, likely to be detected with the planned Square Kilometer Array. We demonstrate that these observations may soon provide the best implementation of the Tolman test to detect any violation of the cosmic distance duality relation.     

The elusive quantal individual

In the formal hedgehog representation of quantum mechanics [5] (ambiguous) weights are derived for hedgehogs with a finite number of questions and answers, in particular applied to spin $\text{1}\text{2}$ and to correlated spin $\text{1}\text{2}$ pairs. Unavoidable negative weights are a clear signal for conceptual difficulties in quantum mechanical interpretation. If these weights had been presupposed to be non-negative, they could have led to Bell-like inequalities inconsistent with quantum mechanics. This is what has happened already in various special models.Owing to the indefinite weights, the hedgehog hypothesis of one-to-one mapping between individual physical samples and individual fictitious hedgehogs cannot be maintained. If no physical interpretation is conceived for the negative weights, the only way to avoid unsolved conceptual difficulties appears to resign (even in the hedgehog representation) to the skeptical ensemble interpretation [1], without theorizing about individual physical samples at all.     

Squeezing of quantal fluctuations

We solve the Schrödinger equation for a harmonic oscillator with time-dependent mass. When this mass increases boundlessly, quantum uncertainties are strongly diminished. This effect is used for a collective theory of charge equilibration. We conclude that present data cannot prove the existence of quantal fluctuations in deep inelastic reactions.     

基于Tolman长度的Lucas-Washburn渗吸模型改进及数值模拟

经典的Lucas-Washburn(L-W)渗吸模型用Young-Laplace方程计算毛管压力, 但该方程在管径细小情形得出的毛管压力值与真实值存在较大偏差。本文运用Tolman长度改进Young-Laplace方程, 提出一种改进的L-W渗吸模型, 并将等截面圆管扩展至任意变化截面圆管, 得到变截面圆管中润湿流体注入长度随时间变化的数学模型。该模型为二阶非线性常微分方程, 无法求出解析解, 为此提出一种数值解法。选取截面变化的毛细管道, 通过数值模拟计算出润湿液体注入长度与时间的对应关系, 对Tolman长度的改进效果进行检验和分析。结果表明: 在研究范围内Tolman长度对L-W渗吸模型的改进效果表现出毛细管道半径越小, 效果越明显的规律。圆管局部缩小能改变渗吸水运动状态, 依次呈现出三种运动模式; 圆管局部扩大会缓慢改变渗吸水运动状态, 只呈现单一运动模式。     

Eikonal description of quantal scattering

Elastic and inelastic quantal scattering is described by a theory in which the contribution of a range of impact parameters to the scattering amplitude is determined by a phase integral (“eikonal”) which is integrated along a real curved “quantal” trajectory. This amplitude reduces to the Glauber expression in the high-energy, forward-angle limit, and to the usual semiclassical amplitude in the classical limit. The formulation can be applied to the study of heavy-ion scattering. The quantal trajectories are investigated analytically for the case of Coulomb scattering. A numerical analysis of elastic ¹⁶O¹⁶O scattering is carried out. The results show appreciable improvement as compared with the Glauber approximation.     

Non-Markovian quantal Brownian motion model

A non-Markovian version of the quantal Brownian motion model is given. The integrodifferential equations of motion are solved, establishing the analytic form of the resolvent poles and analyzing their properties. An explicit investigation of the poles at zero temperature is performed. In this frame a rule can be found that relates the relevant poles of the non-Markovian resolvent to the eigenvalues of the associated Markovian generator of the motion.     

Relation between the generalized Schwarzschild metric and the Tolman metric

In the present paper the relation between the generalized Schwarzschild metric (the Schwarzschild metric including the four-dimensional curvature tensor) [1] and the Tolman metric is considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 29–36, October, 1977.     

A quantal calculation of nucleon transfer contribution in nucleus-nucleus absorptive potential

We present here a model to obtain the quantum-mechanically defined particle-transfer flux in scattering between two heavy nuclei. This flux is calculated from the time-dependent single-particle wave functions in the field of two moving potential pockets. From the calculated flux, we obtain the absorptive potentials for ¹⁶O+⁴⁰Ca and ⁴⁰Ca+⁴⁰Ca, which compare favourably with phenomenological values. In contrast with other similar microscopic calculations, the present results show a weak energy dependence of the absorptive potential as has been observed in phenomenological analyses.     

Average quantal behavior and thermodynamic isolation

We study the thermodynamic concept of isolation. The causal motion of a system that models a thermodynamic universe but nevertheless couples to a surround is reconciled with an increase of entropy-in the manner of the second law of thermodynamics-for the system. The system's ket space isn-dimensional, the surround's isK -dimensional, and the initial state is taken purepure: the tensor product of a puren-state with a pureK-state. Near-maximal entropy is found for the reducedn-state in deep time, first for most random Hamiltonians, then also under restriction to weakn-K coupling-but then with a shortfall of about 1 bit.